We use data from a small aperture array in southern California to quantify variations in source parameter estimates at closely spaced stations (distances ranging from similar to 7 to 350 m) to provide constraints on parameter uncertainties. Many studies do not consider uncertainties in these estimates even though they can be significant and have important implications for studies of earthquake source physics. Here, we estimate seismic source parameters in the frequency domain using empirical Green's function (EGF) methods to remove effects of the travel paths between earthquakes and their recording stations. We examine uncertainties in our estimates by quantifying the resulting distributions over all stations in the array. For coseismic stress drop estimates, we find that minimum uncertainties of similar to 30% of the estimate can be expected. To test the robustness of our results, we explore variations of the dataset using different groupings of stations, different source regions, and different EGF earthquakes. Although these differences affect our absolute estimates of stress drop, they do not greatly influence the spread in our resulting estimates. These sensitivity tests show that station selection is not the primary contribution to the uncertainties in our parameter estimates for single stations. We conclude that establishing reliable methods of estimating uncertainties in source parameter estimates (including corner frequencies, source durations, and coseismic static stress drops) is essential, particularly when the results are used in the comparisons among different studies over a range of earthquake magnitudes and locations.